Answer :
Final answer:
Using the z-score formula, we find that the probability that a lightbulb will last longer than its advertised time is nearly 100%, because its lifespan is typically longer than advertised.
Explanation:
In the field of statistics, we deal with problems like these using a concept known as the z-score. The z-score measures the number of standard deviations an element is from the mean. The formula is z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. In this case, X = 3000 (the advertised time), μ = 3700 (the mean lifespan), and σ = 150 (the standard deviation).
Substituting these into the equation gives us z = (3000 - 3700) / 150 = -4.67. We refer to the z-table to find the corresponding probability, which is virtually zero. Hence, the probability that a bulb lasts less than the advertised time is virtually 100%. Because the question asks for the probability that it lasts longer than the advertised time, we subtract the above probability from 1, which gives us nearly 100%.
Learn more about Probability here:
https://brainly.com/question/22962752
#SPJ11
